Differential Inclusions, Control and Optimization 20 (2000) 195-207
doi: 10.7151/dmdico.1012

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ON WEAK SHARP MINIMA FOR A SPECIAL CLASS OF NONSMOOTH FUNCTIONS

Marcin Studniarski

Faculty of Mathematics, University of Łódź
ul. S. Banacha 22, 90-238 Łódź, Poland

e-mail: marstud@math.uni.lodz.pl

Abstract

We present a characterization of weak sharp local minimizers of order one for a function f:RnR defined by f(x): = max{fi(x)|i = 1,...,p}, where the functions fi are strictly differentiable. It is given in terms of the gradients of fi and the Mordukhovich normal cone to a given set on which f is constant. Then we apply this result to a smooth nonlinear programming problem with constraints.

Keywords and phrases: weak sharp minimizer of order one, maximum function, strictly differentiable function, normal cone.

1991 Mathematics Subject Classification: 49J52; 49K35.

References

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Received 10 December 1999
Revised 7 May 2000